I work for B of A, and to add on to what Derek said, the reason we (and other ) banks are doing this is because there are still a lot of shady lenders out there and they want to make sure that if your lender fails to perform and deliver on a closing then they can step in to preserve the deal. If you are not approvable through B of A then they may consider your offer less qualified and elect to go with an offer that has less question marks

Actually, that is both not discrimination, and is becoming quite common. You can not be mandated to get your loan from a specific lender/broker, but you can be mandated to at least be qualifed by whomever the seller or listing agent prefer.

Best of luck and hope you can get the house.